Regarding the charging problem try different cables, and at least one Apple cable. And what are you using for a power source? If it isn’t an Apple make sure it is spec’d as “USB-C/PD”.
However, if you have data on your phone that is important why aren't you backing it up regularly? Lots of things can go wrong, not just restoring it: Dropping it in a toilet, throwing it under a bus, losing it, having it stolen.
You can back up to your computer, or to iCloud. And you can turn on automatic nightly backup, so you don’t even have to think about it→How to back up your iPhone, iPad, and iPod touch - Apple Support
You can also sync data to iCloud and other devices (which is separate and different from backing up).
iCloud+ has 2 independent functions. iCloud backups, and iCloud sync. It’s confusing because they both have the same name prefix. But they have no connection with each other. Go to Settings/[your name]/iCloud. You will see a bunch of switches (with iOS 16 or later also tap Show All). When you turn on a switch that data type will sync to iCloud. If you do this on multiple devices that share an Apple ID the selected data will sync to all of those devices.
You can also turn on iCloud Backups. This will back up your phone every night if the phone is plugged in, connected to Wi-Fi and locked.
But note that these are independent functions; anything that you sync by the first method will be excluded from the iCloud backups.
You get other benefits with iCloud+
- Hide my Email, which lets you access websites without giving away your primary email account (and also track who they sell your identity to)
- Private Relay, which is sort of a super VPN (at much lower cost than commercial VPN)
- Custom email domain, so you can create a personalized email address that forwards to your Apple ID email (such as jane@doe.com)